Interference cancellation schemes for STBC multiuser systems

1.2 Outline and Contribution of the Thesis 2.2.1 Two Transmit and One Receive Antenna System 2.2.2 Two Transmit and Multiple Receive Antenna System 2.2.3 Multiple Transmit and Multiple R

INTERFERENCE CANCELLATION SCHEMES FOR

STBC MULTIUSER SYSTEMS

VELUPPILLAI MAHINTHAN

(B.Sc.Eng (Hons.), U of Peradeniya)

A THESIS SUBMITTED FOR THE DEGREE OF MASTER OF ENGINEERING

DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING

NATIONAL UNIVERSITY OF SINGAPORE

2003

ACKNOWLEDGEMENT

I would like to express my sincere gratitude to my supervisors Dr B Kannan and Dr

A Nallanathan for providing a stimulating and inspiring research environment It was their constant encouragement, guidance and support that made the pursuit stimulating and rewarding

I would like to thank Institute for Infocomm Research (I2R) and National University of Singapore for providing financial support for my research work

I will always remember my friends - especially Sutha, Kamal, Karthi, Saravanan, Badri, Bijay, Ganesh and Ajeesh - who made life at home, university and research centre an enjoyable experience I also like to thank Niranjan for his assistance on final correction of my thesis

Finally, I would like to thank my parents, Guru and wife for inspiring and encouraging

me throughout my life Without their support and prayers, this would not have been possible

1.2 Outline and Contribution of the Thesis

2.2.1 Two Transmit and One Receive Antenna System

2.2.2 Two Transmit and Multiple Receive Antenna System

2.2.3 Multiple Transmit and Multiple Receive Antenna System

2.2.3.1 Orthogonal Designs for Real Signal Constellations 2.2.3.2 Orthogonal Designs for Complex Signal Constellations 2.2.3.3 STBC System from Orthogonal Designs

2.3 Differential Space-Time Block Coding

CHAPTER 3 OVERVIEW OF INTERFERENCE SUPPRESSION

IN STBC MULITUSER SYSTEMS

3.2 Statistical and Adaptive Signal Processing Techniques

3.2.1 Minimum Mean Square Estimation (MMSE) and Wiener-Hopf

Equations

3.2.2 Least Mean Square (LMS) Algorithm

3.2.3 Linear Least Square Estimation

3.2.4 Recursive Least Square Algorithm

3.3 Interference Suppression using MMSE

3.3.1 System Model

3.3.2 MMSE Interference Suppression

4.3.1 Interference Suppression Based on LSE

4.5 Application of Adaptive Receiver in Multirate Multiuser Systems

4.5.1 Simulation Results of Multirate Systems

CHAPTER 5 AN ITERATIVE INTERFERENCE

CANCELLATION RECEIVER FOR STBC MULTIRATE

MULTIUSER SYSTEMS

5.2.2 Iterative Interference Cancellation

5.2.2.1 Decoding the First User using MMSE

5.2.2.2 Iterative Decoding of the Second User

5.2.2.3 Iterative Decoding of First User

5.3.2 Iterative Interference Cancellation

5.3.2.1 Decoding the High Data Rate User using MMSE

5.3.2.2 Iterative Decoding of the Low Data Rate User

5.3.2.3 Iterative Decoding of the High Data Rate User

SUMMARY

Next generation wireless communication systems are expected to provide a variety of services integrating voice, data and video The rapidly growing demand for these services needs high data rate wireless communication systems with high user capacity

In addition, due to difference in source rate of services, designing a multirate communication system is also an imperative In order to meet this goal, research efforts are carried out to develop efficient coding and modulation schemes along with sophisticated signal and information processing algorithms to improve the quality and spectral efficiency of wireless links However, these developments must cope with critical performance limiting challenges that include multipath fading, multiuser interference, power and size of mobile units

Recently, it has been shown that achievable data rate of wireless communication systems increases dramatically by employing multiple transmit and receive antennas Employing multiple transmit antennas is feasible in mobile communication system because multiple transmit antennas can be deployed at the base station to improves the downlink performance of the system Due to less encoding and decoding complexity, STBC is very popular among transmit diversity systems Most of the STBC schemes relies on that the channel state information available at the receiver This assumption is not valid in real situations As a result, channel estimation techniques are more important to implement the STBC schemes On the other hand, all existing multiuser STBC systems consider equal rate user environment that motivates to explore the

To overcome above-mentioned problems, two novel receivers are proposed Firstly,

An adaptive receiver is proposed to mitigate multiuser interference without any explicit knowledge of channel state information In addition, the proposed adaptive receiver works without any knowledge of the interferer Secondly, an iterative interference cancellation receiver for both equal rate and multi rate space-time block coded multiuser systems is presented Various simulation results demonstrate that both receivers show less computational complexity and better BER performance than that of existing schemes

To overcome above-mentioned problems, two novel receivers are proposed Firstly,

An adaptive receiver is proposed to mitigate multiuser interference without any explicit knowledge of channel state information In addition, the proposed adaptive receiver works without any knowledge of the interferer Secondly, an iterative interference cancellation receiver for both equal rate and multi rate space-time block coded multiuser systems is presented Various simulation results demonstrate that both receivers show less computational complexity and better BER performance than that of existing schemes

NOMENCLATURE

dB Decibel

IIC Iterative Interference Cancellation

iid Independent and Identically Distributed

IS-136 US-TDMA, one of the 2nd generation mobile phone systems IS-54 D-AMPS, digital advanced mobile phone system

MMS Multi Media Messaging

OFDM Orthogonal Frequency Division Multiplexing

ST Space-Time

3.1 Linear filter for MMSE

3.2 Linear filter model for LSE

3.3 MMSE interference suppression system for two users with STBC

4.1 The block diagram of space-time block coded multiuser system

4.2 The structure of proposed adaptive receiver

4.3 Structure of transmitted frame of symbols

4.4 Comparison of the learning curves of RLS and LMS algorithms

4.5 The BER performance of MMSE and adaptive receiver of two co-channel user system

4.6 The BER performance of adaptive receiver and MMSE scheme for two channel user system at fixed SNR

4.7 The BER performance of adaptive receiver and MMSE scheme for multiple channel user systems at fixed SIR and SNR

co-4.8 The BER performance of adaptive receiver of two, three and four co-channel user systems

4.9 The BER performance of MMSE and adaptive receiver of two co-channel user systems; each user equipped with two, three and four transmit antennas, 2bits/s/Hz

4.10 The BER performance of STBC MMSE and LSE-RLS schemes for multirate multiuser systems using 8PSK and QPSK Modulations

4.11 The BER performance of STBC MMSE and LSE-RLS schemes for multirate multiuser systems using BPSK and QPSK Modulations

5.1 The BER performance of STBC-IIC multirate multiuser systems

5.2 The BER performance of STBC-IIC for both multirate and equal rate multiuser systems

LIST OF TABLES

2.1 Space-time block codes for two transmit antenna system

2.2 Real orthogonal transmission matrixes for

2.3 Real generalized orthogonal transmission matrices for

2.4 Unit and half rate complex generalized orthogonal transmission matrices 2.5 ¾ rate complex generalized orthogonal transmission matrices

to improve the quality and spectral efficiency of wireless communication links However, these developments must cope with critical performance limiting challenges that include multipath fading, multiuser interference, power and size of mobile units [1,2]

Mobile communication channels are subject to frequency selective and time selective fading that are induced by multipath propagation, phase shifts and Doppler shifts in the signal The most appropriate way to combat the fading is the exploitation of

information bearing signal to the receiver over independently fading channels There are several ways to provide the independently fading replicas of the information-bearing signal to the receiver Among those, temporal diversity, frequency diversity and space diversity [3] are three main techniques that are widely used in the communication systems To provide the temporal diversity, channel coding is used with appropriate interleaving method The frequency diversity normally introduces redundancy in the frequency domain by transmitting the same information bearing signal over multiple carriers By deploying multiple transmit and receive antennas, which are separated and/or polarized to create independent fading, space diversity can

be achieved

Recently, it has been shown that achievable data rate of wireless communication systems increases dramatically by employing multiple transmit and receive antennas [4-6] In these schemes, it is assumed that the complex-valued propagation coefficients between all pairs of transmit and receive antennas are statistically independent and perfectly known at the receiver Independent channel coefficients are obtained by placing transmit and receive antennas a few wavelengths apart from each other Because of wide antenna separation, the traditional adaptive array concepts of beam forming and directivity cannot be applied to these systems Depending on whether multiple antennas are used for transmission or reception, diversity is classified as transmit antenna diversity and receive antenna diversity In receive antenna diversity schemes, multiple receive antennas are deployed at the receiver to receive multiple copies of transmitted signal which are then properly combined to mitigate the channel fading In fact, receive antenna diversity schemes have been incorporated with the

existing second-generation mobile communication systems such as GSM and IS-136

to improve the mobile to base station transmission (uplink) [7] Due to the size and power limitations of the mobile unit, it is not feasible to deploy the multiple receive antennas at the mobile unit As a result, the base station to mobile transmission (downlink) has some bottleneck in the current mobile communication systems This has motivated the rapidly growing research on transmit antenna diversity

Transmit antenna diversity is feasible in mobile communication system because multiple transmit antennas can be deployed at the base station and that improves the downlink performance of the system A number of transmit antenna diversity schemes has been proposed and that can be divided under two main categories such as open loop and closed loop transmit antenna diversities The open loop scheme transmitter does not require any channel information from the receiver [8-11] On the other hand, the closed loop scheme transmitter relies on the channel information provided by the receiver via a feedback [8,11,12] In fast mobility situations, the transmitter may not

be capable of capturing the channel variations As a result, the usage of open loop schemes is motivated for future wireless communication systems, which are characterized by high mobility

Among open loop transmit diversity schemes space-time coding (STC) is very popular STC relies on multiple antenna transmissions and suitable signal processing technique at the receiver to provide the coding and diversity gains The STC includes space-time trellis coding (STTC) [13] and space-time block coding (STBC) [14-17]

data rate, diversity advantage, coding advantage, and trellis complexity When the number of transmit antennas is fixed, the decoding complexity of STTC increases exponentially with the diversity order and the transmission rate To reduce the decoding complexity at the receiver, Alamouti [14] proposed a remarkable scheme called space-time block coding (STBC) for two transmit antennas It was further extended in [16] for three and four transmit antennas using the theory of orthogonal designs When the channel state information is available at the receiver, the STBC proposed in [14-17] uses a maximum likelihood detection scheme based on linear processing and is able to achieve the full diversity promised by the transmit and receive antennas Recently, STC has been adopted in third generation (3G) cellular standards and proposed in many wireless applications [8,10,11,18,19,20]

A differential detection scheme has been proposed in [21] for two transmit antenna system, where channel state information is not required at the receiver The scheme described in [21] has been further extended to multiple transmit antennas in [22] Due

to the differential detection, the bit error rate (BER) performance of the schemes described in [21] and [22] is 3 dB worse than that of the scheme proposed in [14] and [16], respectively A new detection schemes for STBC without channel estimation but not fully differential scheme is proposed in [23] This scheme has more than 3 dB penalty compared to coherent detection in [14] In [24], a new and general approach to differential modulation for multiple antennas based on group codes was presented This approach can be applied to any number of antennas, and any signal constellation

A non-differential approach to transmit diversity when the channel is unknown is

reported in [25] But the schemes described in [24] and [25] have both exponential encoding and decoding complexities

So far, most of the schemes assume that channel is frequency non-selective Unfortunately, in the broadband wireless communication systems, the channel response over the occupied bandwidth is generally neither flat in frequency nor static across time In broadband wireless communication systems symbol duration is smaller than the channel delay spread which results the channel to be frequency selective It is important to investigate the STC in the frequency selective environments The effects

of multipath on the performance of STTC are studied in [26] for a slowly varying channel Furthermore, it is proved that the presence of multipath does not decrease the diversity order of STTC Results in [26] suggest that STTC in frequency selective fading channels may achieve higher diversity advantage than those in flat fading channels providing that the channel state information is available at the receiver However, the scheme works based on ML decoding that is computationally expensive

In this situation, feasible STC designs for frequency selective channels are important

Since the introduction of STBC by Alamouti in [14], the following transmissions schemes have been proposed to extend the STBC to frequency selective channels One approach, with lower receiver complexity, is to employ orthogonal frequency division multiplexing (OFDM), which converts the frequency selective channel into a set of flat fading sub channels through inverse fast Fourier transform (IFFT) and cyclic prefix (CP) insertion at the transmitter CP removal and fast Fourier transform (FFT) are used

applied on each OFDM sub carrier [26-28] Space-time codes designed for flat-fading channels can be utilized to achieve full multi antenna diversity in frequency selective fading channels [26] But, the potential diversity gain available in multipath propagation has not been addressed Recently, in OFDM based systems, it was produced in [30-33] that it is possible to achieve both multi antenna diversity and multipath diversity gains that is equal to the product of number of transmit antennas, number of receive antennas and number of finite impulse response (FIR) channel taps

Limitation of all multi carrier (OFDM) based STC transmissions is their non-constant modulus, which necessitates power amplifier back off, and thus reduces power efficiency In addition, multi carrier schemes are more sensitive to inter carrier interference Above factors motivate the importance of having single carrier STBC transmission schemes [34-40] for frequency selective channels These single carrier based schemes are based on frequency domain equalization (FDE) of received signal

at the receiver that can be employed by taking FFT and then equalizing the received signal block Finally, equalized received signals go through IFFT block and then decision is made in the time domain using a slicer as described in [34] A generalized transmission scheme for single carrier STBC is proposed in [38-40] that subsume those in [34-37] as special cases Furthermore, it is proved in [34] that the diversity order is N N L t r( + , where 1) N is the number of transmit antennas, t N is the number r

of receive antennas and L is the number of taps in the FIR filter model of the channel

Co-channel interference is generally recognized as one of the factors that limit the capacity and the transmission quality in wireless communications An appropriate

understanding of the interference is extremely important when analyzing and designing multiuser wireless systems or exploring techniques that mitigate the undesirable effects of co-channel users [41-43] By exploiting the spatial and temporal structure of the STC, interference from the co-channel users can be suppressed An interference cancellation scheme for STBC multiuser systems with 2 synchronous co-channel users, each is equipped with 2 transmit antennas, has been presented for flat fading channels in [44] This scheme is based on minimum mean square error (MMSE) and ML detection at the receiver Further, this scheme has been extended in [45] for more than two synchronous co-channel users; where each user is equipped with more than 2 transmit antennas The effectiveness of the interference suppression

of these STBC co-channel multiuser systems relies on accurate channel estimates available at the receiver An interference cancellation method based on zero forcing (ZF) method is presented in [46] for single carrier STBC-FDE [32] two-user system

Most of above schemes relies on the fact that the channel state information is available

at the receiver This assumption is not valid in real situations As a result, channel estimation techniques are more important I the implementation of the above schemes

A joint channel estimation and co-channel interference suppression scheme has been presented in [47,48] for wireless time division multiple access (TDMA) systems equipped with multiple transmits and receives antennas in frequency selective channel This scheme is able to mitigate interference of various origins, including inter-symbol interference and co-channel interference

An effort has been taken in this thesis to present an overview of interference cancellation schemes in space-time coded multiuser systems and to specifically solve the following problems:

1 Jointly estimate the channel and suppress the interference of STBC multiuser systems by using an adaptive receiver scheme that operates based on least square error (LSE) and recursive least square (RLS) signal processing techniques

2 Above problem is extended for multirate multiuser systems where an iterative interference cancellation (IIC) scheme is used based on minimum mean square error (MMSE) and maximum likelihood (ML) techniques

1.2 Outline and Contributions of the Thesis

Chapter 2 presents overview of space-time block coding schemes Firstly, space-time coding schemes for two transmit antennas and multiple transmit antennas are described Secondly, Importance of a differential detection scheme for space-time block coding is analyzed and presented Finally, comparisons of simulation results are given

Chapter 3 sets up the framework needed to introduce the new interference cancellation schemes for space-time block coded multiuser systems It starts with a review of statistical and adaptive signal processing concepts such as MMSE, LMS, LSE and RLS Then, existing interference cancellation techniques for STBC multiuser systems based on MMSE are described Overview of signal processing techniques and existing interference cancellation schemes simplify the understanding of the derivation of proposed schemes in the following chapters

An adaptive receiver is presented in chapter 4 In this adaptive receiver, multiuser interference is cancelled without any explicit knowledge of channel state information The computational complexity of the proposed adaptive receiver is less than that of the MMSE interference cancellation scheme On the other hand, due to the weight estimation errors, the BER performance of the adaptive receiver is little bit worse than the BER performance of the MMSE interference cancellation scheme It is also noted that the proposed adaptive receiver works without any explicit knowledge of the channel and interferer Finally, chapter 4 presents the application of adaptive receiver scheme for multirate multiuser systems

Iterative interference cancellation scheme (IIC) for both equal rate and multi rate space-time block coded multiuser systems is presented in chapter 5 The proposed IIC scheme is derived based on MMSE interference cancellation and ML decoding The IIC scheme outperforms the conventional MMSE interference cancellation schemes

In addition, it is shown that the BER performance of IIC multirate systems is better

than that of IIC equal rate systems The simulation results and comparisons show the effectiveness of the proposed scheme

Chapter 6 summarizes the thesis and discusses the possible extensions and directions

of future research In particular, some aspects and open problems pertaining to the interference cancellation and channel estimation of the STBC systems in frequency selective channels are discussed

Some results presented in this thesis can be found in the following publications

V Mahinthan, B Kannan, and A Nallanathan, “Joint channel estimation and interference cancellation in space-time coded multiuser systems,” Proc IEEE Mobile Wireless Communications Networks, Stockholm, Sweden Sep 2002

V Mahinthan, B Kannan, and A Nallanathan, “Adaptive channel estimation and interference suppression in space-time coded multiuser systems,” Proc IEEE GLOBECOM, Taipei, Taiwan Nov 2002

V Mahinthan, B Kannan, and A Nallanathan, “Performance of LSE-RLS based interference cancellation scheme for STBC multiuser systems,” IEE Electronic Letters, Dec 2002, Vol 38, No 25, pp 1729-1730

V Mahinthan, B Kannan, and A Nallanathan, “An adaptive receiver for space-time block coded multiuser systems,” Submitted to the IEEE Transactions on Communications

V Mahinthan, B Kannan, and A Nallanathan, “An Iterative Interference Cancellation Scheme for STBC Multirate Multiuser Systems,” Submitted to IEEE Communication Letters

CHAPTER 2

OVERVIEW OF SPACE-TIME BLOCK CODES

Space-time block coding has been introduced recently and has sparked a wide interest among the research communities as it promises to increase transmission rates significantly in wireless communications In this chapter, the system model and receiver structure of the STBC and DSTBC are reviewed In addition, advantages and inherent problems of STBC and DSTBC schemes are discussed

2.1 Introduction

Alamouti [14] proposed a simple transmit diversity scheme called space-time block codes, which fully exploits the spatial diversity offered by two transmit and multiple receive antennas and improves the overall performance of the wireless communication systems It was further extended in [16] for three and four antennas using the theory of orthogonal designs When channel state information is available at the receiver, the STBC proposed in [14-16] uses a maximum likelihood detection based on linear processing at the receiver The differential detection schemes have been proposed in [21] and [22] for the STBC schemes presented in [14] and [16] respectively, where

channel state information are not required at the receiver But the BER performances

of the differential detection schemes are 3 dB worse than that of respective coherent schemes

2.2 Space-Time Block Coding

2.2.1 Two Transmit and One Receive Antenna System

Fig 2.1 Space-time block coded transmit diversity system for two transmit and one

receive antennas

Consider the transmit diversity scheme with 2 transmit and 1 receive antennas as shown in Fig 2.1, where two transmit antennas are well separated to get independent fading At a given symbol period T two digitally modulated signals are s

simultaneously transmitted from the two antennas As given in the Table 2.1, symbols

1

c and c are transmitted from antenna 1 and antenna 2 respectively During the next 2

symbol period signal − is transmitted from antenna 1, and signal c2* *

transmit antenna to the receive antenna The received signal over two consecutive symbol periods is defined as r and 1 r 2

Table 2.1 Space-time block codes for two transmit antenna system

Transmit Antenna Time t Time t T+ s

Defining the received signal vector, r= ⎣⎡r1 r2*⎤⎦T, the code symbols vector [ 1 2]

Hence, channel matrix H is orthogonal H H * =(h12+ h2 2)I 2

By multiplying the receive signal by conjugate transpose of the channel matrix,

2.2.2 Two Transmit and Multiple Receive Antenna System

Fig 2.2 Space-time block coded transmit diversity system for two transmit and

multiple receive antennas

Consider the transmit diversity scheme with 2 transmit and N receive antennas as r

shown in Fig 2.2 where both transmit and receive antennas are well separated to get independent fading As written in (2.3), the received signal vector r at m th

m receive

antenna can be written as,

m= m + m

where η is the noise vector at the m th

m receive antenna and

Hence, channel matrix H is orthogonal m H H m * m =(h1,m 2+ h2,m 2)I 2

By multiplying the receive signal by conjugate transpose of the channel matrix,

In the case of N receive antennas, 2 r N diversity can be achieved as shown in (2.10) r

2.2.3 Multiple Transmit and Multiple Receive Antenna System

The space-time block coding transmission matrix

t N

G for more than two transmit

antenna system is designed based on the classical mathematical framework of orthogonal designs [16] However, STBC can be constructed using orthogonal designs for few sporadic values of N (number of transmit antennas) It is shown in [16] that t

STBC for any signal constellations and any numbers of transmit antennas can be generated by the generalization of orthogonal designs

As stated in the literature, a p N× t transmission matrix

t N

G defines the STBC The

entries of the real transmission matrix are positive or negative values of c where l

1, 2

l = L On the other hand, the entries of the complex transmission matrix are linear combination of the variables c and their conjugates The rate l S of the code is defined as S =L p/

2.2.3.1 Orthogonal Designs for Real Signal Constellations

The real orthogonal designs only exist for small number of dimensions A real orthogonal design of size N is an t N t×N t orthogonal transmission matrix which exists only for N t =2, 4,8 Some examples are given in Table 2.2 The limitations of providing transmit diversity through linear processing based on orthogonal square transmission matrix can be subdued by the generalized orthogonal designs [16] The non-square orthogonal transmission matrix of generalized orthogonal designs for

2.2.3.2 Orthogonal Designs for Complex Signal Constellations

The complex orthogonal designs only exist for N t = The STBC proposed by 2Alamouti [14] uses the complex orthogonal design for N t = To overcome the 2barrier of complex orthogonal designs, a generalized complex orthogonal design is proposed in [16] Furthermore, it is proved that a half rate generalized complex orthogonal transmission matrices exist for any numbers of transmit antennas Some examples are given in Table 2.4 Specially, ¾ rate generalized complex orthogonal transmission matrices are provided for three and four transmit antennas in Table 2.5

Table 2.3 Real generalized orthogonal transmission matrices for N t =3, 5, 6, 7

Table 2.4 – Unit and Half rate complex generalized orthogonal transmission matrices

2.2.3.3 STBC System from Orthogonal Designs

Fig 2.3 Space-time block coded transmit diversity system for multiple transmit and

multiple receive antennas

Consider a transmit and receive diversity system as shown Fig 2.3 where the transmitter is equipped with N transmit antennas and receiver is equipped with t N r

receive antennas Both transmit antennas and receive antennas are well separated from each other to obtain independent channel fading Further, the channel fading is assumed to be quasi static so that the path gains are constant over a frame and vary from one frame to another

Consider the system using the STBC defined by the transmission matrix

t N

G and simultaneously transmitted from the N transmit antennas The flat t

fading path gain h j k, is defined as from j transmit antenna of the transmitter to the th

Based on the system mentioned above, the received signal at k antenna during t time th

slot, r t k, is given by

1

t N

Assuming coherent detection and perfect channel information is available at the receiver The decision metric can be computed by ML rule [49],

be taken in favor of the codeword that minimizes the decision metric given in (2.12)

2.3 Differential Space-Time Block Coding

Space-time block coding schemes given in section 2.2 assume perfect channel knowledge is available at the receiver to decode the received signal However, in real situation the channel knowledge is not known perfectly This problem is subdued in

the training symbols or pilot symbols This method will be covered in the next chapters Another method is differential detection scheme where the symbols are decoded without the channel knowledge Differential detection schemes are widely used for single transmit antenna systems Furthermore, the differential detection schemes are used in the IEEE IS-54 standard This motivates the generalization of the differential detection schemes for the multiple transmit antenna schemes that might be used in next generation communication systems such as wideband code division multiple access (WCDMA) [56] and CDMA 2000 [56]

A partial differential solution for Alamouti scheme [14] is proposed in [23], where symbols are decoded at the receiver without the channel knowledge In the mean time, known symbols should be transmitted at the beginning of the transmission of a frame The scheme given in [23] can be characterized as joint channel and symbol estimation

In this scheme [23], detected symbols at time slot t are used to detect the symbols at

time slot t+1 This joint channel and symbol estimation can lead to error propagation

A truly differential detection scheme has been proposed in [21] for two transmit antenna system and it is further extended to multiple transmit antennas in [22] Detail description of the scheme given in [21] is presented and their performance is analyzed

in the following sections

2.3.1 Encoding of DSTBC

The transmitter starts to transmit the symbols as Alamouti codes for first and second symbol duration of the frame These arbitrary symbols c1and c2 at time 1 and symbols

2t−1 from transmit antennas 1 and 2 respectively and − and c*2t *

2t 1

c − are transmitted at time 2t from transmit antennas 1 and 2 respectively Subsequently, the symbols c2t+1

and c2t+2 are encoded by differential encoder as given in the following equation:

c + are mapped from gray coded signal constellations [50]

For example, consider the BPSK modulation scheme with constellation points

c − =c = Then the mapping M Bits( )=(A Bits( ) B Bits( ))

maps the two input bits from the set ν ={(1, 0), (0,1), ( 1, 0), (0, 1)− − }as given below,

( )

(11) 1 0

By using the mapped information of A Bits and (( ) B Bits in the equation (2.13), ) c2t+1

and c2t+2 are calculated to transmit at time 2t+1 from antennas 1 and 2 respectively

At time 2t+2, −c*2t+2 and c*2t+1 are transmitted from antennas 1 and 2 respectively This process is continued until the end of the frame

Next, the receiver needs the second term in the right side of (2.13)

From the equations (2.17) and (2.18),

To compute(A Bits( ) B Bits( )), the receiver now computes vector ν , that is closest to

(ℜ1 ℜ2) Once the vector is computed, the inverse mapping of M Bits is applied ( )and the transmitted bits are decoded

DSTBC for multiple transmit antennas can be extended from above derivations that is given in [22] based on the theory of generalized orthogonal designs

2.4 Simulation

In this section, BER performance of the STBC and DSTBC schemes are obtained using Monte-Carlo simulations Alamouti codes for two transmit antenna diversity and half rate complex generalized orthogonal designs for three and four transmit antenna diversity are considered The transmission matrices for the simulation are given in

Table 2.4 The channel is considered as Rayleigh quasi-static flat fading The amplitude of fading from each transmit antenna to each receive antenna is assumed to

be mutually uncorrelated and i.i.d Furthermore, the transmitted power is shared equally between transmit antennas in order to ensure the same total power as one transmit antenna scheme In the STBC cases, perfect channel knowledge is assumed at the receiver to decode the signals

Fig 2.4: The BER performance of STBC scheme for two transmit antennas using

BPSK modulation scheme

In Fig 2.4, BER performance of the STBC scheme (Alamouti scheme) for both two transmit one receive and two transmit two receive antenna systems are compared with